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isl_printer_print_pw_aff: simplify domain expression in C format
[isl.git] / isl_aff.c
blob846556dcea591e93cfb2c75c0562f68a13c687ff
1 /*
2 * Copyright 2011 INRIA Saclay
3 * Copyright 2011 Sven Verdoolaege
4 *
5 * Use of this software is governed by the GNU LGPLv2.1 license
6 *
7 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
8 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
9 * 91893 Orsay, France
10 */
11
12 #include <isl_ctx_private.h>
13 #include <isl_map_private.h>
14 #include <isl_aff_private.h>
15 #include <isl_space_private.h>
16 #include <isl_local_space_private.h>
17 #include <isl_mat_private.h>
18 #include <isl_list_private.h>
19 #include <isl/constraint.h>
20 #include <isl/seq.h>
21 #include <isl/set.h>
22 #include <isl_config.h>
23
24 __isl_give isl_aff *isl_aff_alloc_vec(__isl_take isl_local_space *ls,
25 __isl_take isl_vec *v)
26 {
27 isl_aff *aff;
28
29 if (!ls || !v)
30 goto error;
31
32 aff = isl_calloc_type(v->ctx, struct isl_aff);
33 if (!aff)
34 goto error;
35
36 aff->ref = 1;
37 aff->ls = ls;
38 aff->v = v;
39
40 return aff;
41 error:
42 isl_local_space_free(ls);
43 isl_vec_free(v);
44 return NULL;
45 }
46
47 __isl_give isl_aff *isl_aff_alloc(__isl_take isl_local_space *ls)
48 {
49 isl_ctx *ctx;
50 isl_vec *v;
51 unsigned total;
52
53 if (!ls)
54 return NULL;
55
56 ctx = isl_local_space_get_ctx(ls);
57 if (!isl_local_space_divs_known(ls))
58 isl_die(ctx, isl_error_invalid, "local space has unknown divs",
59 goto error);
60 if (!isl_local_space_is_set(ls))
61 isl_die(ctx, isl_error_invalid,
62 "domain of affine expression should be a set",
63 goto error);
64
65 total = isl_local_space_dim(ls, isl_dim_all);
66 v = isl_vec_alloc(ctx, 1 + 1 + total);
67 return isl_aff_alloc_vec(ls, v);
68 error:
69 isl_local_space_free(ls);
70 return NULL;
71 }
72
73 __isl_give isl_aff *isl_aff_zero_on_domain(__isl_take isl_local_space *ls)
74 {
75 isl_aff *aff;
76
77 aff = isl_aff_alloc(ls);
78 if (!aff)
79 return NULL;
80
81 isl_int_set_si(aff->v->el[0], 1);
82 isl_seq_clr(aff->v->el + 1, aff->v->size - 1);
83
84 return aff;
85 }
86
87 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff)
88 {
89 if (!aff)
90 return NULL;
91
92 aff->ref++;
93 return aff;
94 }
95
96 __isl_give isl_aff *isl_aff_dup(__isl_keep isl_aff *aff)
97 {
98 if (!aff)
99 return NULL;
100
101 return isl_aff_alloc_vec(isl_local_space_copy(aff->ls),
102 isl_vec_copy(aff->v));
103 }
104
105 __isl_give isl_aff *isl_aff_cow(__isl_take isl_aff *aff)
106 {
107 if (!aff)
108 return NULL;
109
110 if (aff->ref == 1)
111 return aff;
112 aff->ref--;
113 return isl_aff_dup(aff);
114 }
115
116 void *isl_aff_free(__isl_take isl_aff *aff)
117 {
118 if (!aff)
119 return NULL;
120
121 if (--aff->ref > 0)
122 return NULL;
123
124 isl_local_space_free(aff->ls);
125 isl_vec_free(aff->v);
126
127 free(aff);
128
129 return NULL;
130 }
131
132 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff)
133 {
134 return aff ? isl_local_space_get_ctx(aff->ls) : NULL;
135 }
136
137 /* Externally, an isl_aff has a map space, but internally, the
138 * ls field corresponds to the domain of that space.
139 */
140 int isl_aff_dim(__isl_keep isl_aff *aff, enum isl_dim_type type)
141 {
142 if (!aff)
143 return 0;
144 if (type == isl_dim_out)
145 return 1;
146 if (type == isl_dim_in)
147 type = isl_dim_set;
148 return isl_local_space_dim(aff->ls, type);
149 }
150
151 __isl_give isl_space *isl_aff_get_domain_space(__isl_keep isl_aff *aff)
152 {
153 return aff ? isl_local_space_get_space(aff->ls) : NULL;
154 }
155
156 __isl_give isl_space *isl_aff_get_space(__isl_keep isl_aff *aff)
157 {
158 isl_space *space;
159 if (!aff)
160 return NULL;
161 space = isl_local_space_get_space(aff->ls);
162 space = isl_space_from_domain(space);
163 space = isl_space_add_dims(space, isl_dim_out, 1);
164 return space;
165 }
166
167 __isl_give isl_local_space *isl_aff_get_domain_local_space(
168 __isl_keep isl_aff *aff)
169 {
170 return aff ? isl_local_space_copy(aff->ls) : NULL;
171 }
172
173 __isl_give isl_local_space *isl_aff_get_local_space(__isl_keep isl_aff *aff)
174 {
175 isl_local_space *ls;
176 if (!aff)
177 return NULL;
178 ls = isl_local_space_copy(aff->ls);
179 ls = isl_local_space_from_domain(ls);
180 ls = isl_local_space_add_dims(ls, isl_dim_out, 1);
181 return ls;
182 }
183
184 /* Externally, an isl_aff has a map space, but internally, the
185 * ls field corresponds to the domain of that space.
186 */
187 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
188 enum isl_dim_type type, unsigned pos)
189 {
190 if (!aff)
191 return NULL;
192 if (type == isl_dim_out)
193 return NULL;
194 if (type == isl_dim_in)
195 type = isl_dim_set;
196 return isl_local_space_get_dim_name(aff->ls, type, pos);
197 }
198
199 __isl_give isl_aff *isl_aff_reset_domain_space(__isl_take isl_aff *aff,
200 __isl_take isl_space *dim)
201 {
202 aff = isl_aff_cow(aff);
203 if (!aff || !dim)
204 goto error;
205
206 aff->ls = isl_local_space_reset_space(aff->ls, dim);
207 if (!aff->ls)
208 return isl_aff_free(aff);
209
210 return aff;
211 error:
212 isl_aff_free(aff);
213 isl_space_free(dim);
214 return NULL;
215 }
216
217 /* Reset the space of "aff". This function is called from isl_pw_templ.c
218 * and doesn't know if the space of an element object is represented
219 * directly or through its domain. It therefore passes along both.
220 */
221 __isl_give isl_aff *isl_aff_reset_space_and_domain(__isl_take isl_aff *aff,
222 __isl_take isl_space *space, __isl_take isl_space *domain)
223 {
224 isl_space_free(space);
225 return isl_aff_reset_domain_space(aff, domain);
226 }
227
228 /* Reorder the coefficients of the affine expression based
229 * on the given reodering.
230 * The reordering r is assumed to have been extended with the local
231 * variables.
232 */
233 static __isl_give isl_vec *vec_reorder(__isl_take isl_vec *vec,
234 __isl_take isl_reordering *r, int n_div)
235 {
236 isl_vec *res;
237 int i;
238
239 if (!vec || !r)
240 goto error;
241
242 res = isl_vec_alloc(vec->ctx,
243 2 + isl_space_dim(r->dim, isl_dim_all) + n_div);
244 isl_seq_cpy(res->el, vec->el, 2);
245 isl_seq_clr(res->el + 2, res->size - 2);
246 for (i = 0; i < r->len; ++i)
247 isl_int_set(res->el[2 + r->pos[i]], vec->el[2 + i]);
248
249 isl_reordering_free(r);
250 isl_vec_free(vec);
251 return res;
252 error:
253 isl_vec_free(vec);
254 isl_reordering_free(r);
255 return NULL;
256 }
257
258 /* Reorder the dimensions of the domain of "aff" according
259 * to the given reordering.
260 */
261 __isl_give isl_aff *isl_aff_realign_domain(__isl_take isl_aff *aff,
262 __isl_take isl_reordering *r)
263 {
264 aff = isl_aff_cow(aff);
265 if (!aff)
266 goto error;
267
268 r = isl_reordering_extend(r, aff->ls->div->n_row);
269 aff->v = vec_reorder(aff->v, isl_reordering_copy(r),
270 aff->ls->div->n_row);
271 aff->ls = isl_local_space_realign(aff->ls, r);
272
273 if (!aff->v || !aff->ls)
274 return isl_aff_free(aff);
275
276 return aff;
277 error:
278 isl_aff_free(aff);
279 isl_reordering_free(r);
280 return NULL;
281 }
282
283 __isl_give isl_aff *isl_aff_align_params(__isl_take isl_aff *aff,
284 __isl_take isl_space *model)
285 {
286 if (!aff || !model)
287 goto error;
288
289 if (!isl_space_match(aff->ls->dim, isl_dim_param,
290 model, isl_dim_param)) {
291 isl_reordering *exp;
292
293 model = isl_space_drop_dims(model, isl_dim_in,
294 0, isl_space_dim(model, isl_dim_in));
295 model = isl_space_drop_dims(model, isl_dim_out,
296 0, isl_space_dim(model, isl_dim_out));
297 exp = isl_parameter_alignment_reordering(aff->ls->dim, model);
298 exp = isl_reordering_extend_space(exp,
299 isl_aff_get_domain_space(aff));
300 aff = isl_aff_realign_domain(aff, exp);
301 }
302
303 isl_space_free(model);
304 return aff;
305 error:
306 isl_space_free(model);
307 isl_aff_free(aff);
308 return NULL;
309 }
310
311 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff)
312 {
313 if (!aff)
314 return -1;
315
316 return isl_seq_first_non_zero(aff->v->el + 1, aff->v->size - 1) < 0;
317 }
318
319 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1, __isl_keep isl_aff *aff2)
320 {
321 int equal;
322
323 if (!aff1 || !aff2)
324 return -1;
325
326 equal = isl_local_space_is_equal(aff1->ls, aff2->ls);
327 if (equal < 0 || !equal)
328 return equal;
329
330 return isl_vec_is_equal(aff1->v, aff2->v);
331 }
332
333 int isl_aff_get_denominator(__isl_keep isl_aff *aff, isl_int *v)
334 {
335 if (!aff)
336 return -1;
337 isl_int_set(*v, aff->v->el[0]);
338 return 0;
339 }
340
341 int isl_aff_get_constant(__isl_keep isl_aff *aff, isl_int *v)
342 {
343 if (!aff)
344 return -1;
345 isl_int_set(*v, aff->v->el[1]);
346 return 0;
347 }
348
349 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
350 enum isl_dim_type type, int pos, isl_int *v)
351 {
352 if (!aff)
353 return -1;
354
355 if (type == isl_dim_out)
356 isl_die(aff->v->ctx, isl_error_invalid,
357 "output/set dimension does not have a coefficient",
358 return -1);
359 if (type == isl_dim_in)
360 type = isl_dim_set;
361
362 if (pos >= isl_local_space_dim(aff->ls, type))
363 isl_die(aff->v->ctx, isl_error_invalid,
364 "position out of bounds", return -1);
365
366 pos += isl_local_space_offset(aff->ls, type);
367 isl_int_set(*v, aff->v->el[1 + pos]);
368
369 return 0;
370 }
371
372 __isl_give isl_aff *isl_aff_set_denominator(__isl_take isl_aff *aff, isl_int v)
373 {
374 aff = isl_aff_cow(aff);
375 if (!aff)
376 return NULL;
377
378 aff->v = isl_vec_cow(aff->v);
379 if (!aff->v)
380 return isl_aff_free(aff);
381
382 isl_int_set(aff->v->el[0], v);
383
384 return aff;
385 }
386
387 __isl_give isl_aff *isl_aff_set_constant(__isl_take isl_aff *aff, isl_int v)
388 {
389 aff = isl_aff_cow(aff);
390 if (!aff)
391 return NULL;
392
393 aff->v = isl_vec_cow(aff->v);
394 if (!aff->v)
395 return isl_aff_free(aff);
396
397 isl_int_set(aff->v->el[1], v);
398
399 return aff;
400 }
401
402 __isl_give isl_aff *isl_aff_add_constant(__isl_take isl_aff *aff, isl_int v)
403 {
404 if (isl_int_is_zero(v))
405 return aff;
406
407 aff = isl_aff_cow(aff);
408 if (!aff)
409 return NULL;
410
411 aff->v = isl_vec_cow(aff->v);
412 if (!aff->v)
413 return isl_aff_free(aff);
414
415 isl_int_addmul(aff->v->el[1], aff->v->el[0], v);
416
417 return aff;
418 }
419
420 __isl_give isl_aff *isl_aff_add_constant_si(__isl_take isl_aff *aff, int v)
421 {
422 isl_int t;
423
424 isl_int_init(t);
425 isl_int_set_si(t, v);
426 aff = isl_aff_add_constant(aff, t);
427 isl_int_clear(t);
428
429 return aff;
430 }
431
432 __isl_give isl_aff *isl_aff_set_constant_si(__isl_take isl_aff *aff, int v)
433 {
434 aff = isl_aff_cow(aff);
435 if (!aff)
436 return NULL;
437
438 aff->v = isl_vec_cow(aff->v);
439 if (!aff->v)
440 return isl_aff_free(aff);
441
442 isl_int_set_si(aff->v->el[1], v);
443
444 return aff;
445 }
446
447 __isl_give isl_aff *isl_aff_set_coefficient(__isl_take isl_aff *aff,
448 enum isl_dim_type type, int pos, isl_int v)
449 {
450 if (!aff)
451 return NULL;
452
453 if (type == isl_dim_out)
454 isl_die(aff->v->ctx, isl_error_invalid,
455 "output/set dimension does not have a coefficient",
456 return isl_aff_free(aff));
457 if (type == isl_dim_in)
458 type = isl_dim_set;
459
460 if (pos >= isl_local_space_dim(aff->ls, type))
461 isl_die(aff->v->ctx, isl_error_invalid,
462 "position out of bounds", return isl_aff_free(aff));
463
464 aff = isl_aff_cow(aff);
465 if (!aff)
466 return NULL;
467
468 aff->v = isl_vec_cow(aff->v);
469 if (!aff->v)
470 return isl_aff_free(aff);
471
472 pos += isl_local_space_offset(aff->ls, type);
473 isl_int_set(aff->v->el[1 + pos], v);
474
475 return aff;
476 }
477
478 __isl_give isl_aff *isl_aff_set_coefficient_si(__isl_take isl_aff *aff,
479 enum isl_dim_type type, int pos, int v)
480 {
481 if (!aff)
482 return NULL;
483
484 if (type == isl_dim_out)
485 isl_die(aff->v->ctx, isl_error_invalid,
486 "output/set dimension does not have a coefficient",
487 return isl_aff_free(aff));
488 if (type == isl_dim_in)
489 type = isl_dim_set;
490
491 if (pos >= isl_local_space_dim(aff->ls, type))
492 isl_die(aff->v->ctx, isl_error_invalid,
493 "position out of bounds", return isl_aff_free(aff));
494
495 aff = isl_aff_cow(aff);
496 if (!aff)
497 return NULL;
498
499 aff->v = isl_vec_cow(aff->v);
500 if (!aff->v)
501 return isl_aff_free(aff);
502
503 pos += isl_local_space_offset(aff->ls, type);
504 isl_int_set_si(aff->v->el[1 + pos], v);
505
506 return aff;
507 }
508
509 __isl_give isl_aff *isl_aff_add_coefficient(__isl_take isl_aff *aff,
510 enum isl_dim_type type, int pos, isl_int v)
511 {
512 if (!aff)
513 return NULL;
514
515 if (type == isl_dim_out)
516 isl_die(aff->v->ctx, isl_error_invalid,
517 "output/set dimension does not have a coefficient",
518 return isl_aff_free(aff));
519 if (type == isl_dim_in)
520 type = isl_dim_set;
521
522 if (pos >= isl_local_space_dim(aff->ls, type))
523 isl_die(aff->v->ctx, isl_error_invalid,
524 "position out of bounds", return isl_aff_free(aff));
525
526 aff = isl_aff_cow(aff);
527 if (!aff)
528 return NULL;
529
530 aff->v = isl_vec_cow(aff->v);
531 if (!aff->v)
532 return isl_aff_free(aff);
533
534 pos += isl_local_space_offset(aff->ls, type);
535 isl_int_addmul(aff->v->el[1 + pos], aff->v->el[0], v);
536
537 return aff;
538 }
539
540 __isl_give isl_aff *isl_aff_add_coefficient_si(__isl_take isl_aff *aff,
541 enum isl_dim_type type, int pos, int v)
542 {
543 isl_int t;
544
545 isl_int_init(t);
546 isl_int_set_si(t, v);
547 aff = isl_aff_add_coefficient(aff, type, pos, t);
548 isl_int_clear(t);
549
550 return aff;
551 }
552
553 __isl_give isl_aff *isl_aff_get_div(__isl_keep isl_aff *aff, int pos)
554 {
555 if (!aff)
556 return NULL;
557
558 return isl_local_space_get_div(aff->ls, pos);
559 }
560
561 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff)
562 {
563 aff = isl_aff_cow(aff);
564 if (!aff)
565 return NULL;
566 aff->v = isl_vec_cow(aff->v);
567 if (!aff->v)
568 return isl_aff_free(aff);
569
570 isl_seq_neg(aff->v->el + 1, aff->v->el + 1, aff->v->size - 1);
571
572 return aff;
573 }
574
575 __isl_give isl_aff *isl_aff_normalize(__isl_take isl_aff *aff)
576 {
577 if (!aff)
578 return NULL;
579 aff->v = isl_vec_normalize(aff->v);
580 if (!aff->v)
581 return isl_aff_free(aff);
582 return aff;
583 }
584
585 /* Given f, return floor(f).
586 * If f is an integer expression, then just return f.
587 * Otherwise, if f = g/m, write g = q m + r,
588 * create a new div d = [r/m] and return the expression q + d.
589 * The coefficients in r are taken to lie between -m/2 and m/2.
590 */
591 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff)
592 {
593 int i;
594 int size;
595 isl_ctx *ctx;
596 isl_vec *div;
597
598 if (!aff)
599 return NULL;
600
601 if (isl_int_is_one(aff->v->el[0]))
602 return aff;
603
604 aff = isl_aff_cow(aff);
605 if (!aff)
606 return NULL;
607
608 aff->v = isl_vec_cow(aff->v);
609 div = isl_vec_copy(aff->v);
610 div = isl_vec_cow(div);
611 if (!div)
612 return isl_aff_free(aff);
613
614 ctx = isl_aff_get_ctx(aff);
615 isl_int_fdiv_q(aff->v->el[0], aff->v->el[0], ctx->two);
616 for (i = 1; i < aff->v->size; ++i) {
617 isl_int_fdiv_r(div->el[i], div->el[i], div->el[0]);
618 isl_int_fdiv_q(aff->v->el[i], aff->v->el[i], div->el[0]);
619 if (isl_int_gt(div->el[i], aff->v->el[0])) {
620 isl_int_sub(div->el[i], div->el[i], div->el[0]);
621 isl_int_add_ui(aff->v->el[i], aff->v->el[i], 1);
622 }
623 }
624
625 aff->ls = isl_local_space_add_div(aff->ls, div);
626 if (!aff->ls)
627 return isl_aff_free(aff);
628
629 size = aff->v->size;
630 aff->v = isl_vec_extend(aff->v, size + 1);
631 if (!aff->v)
632 return isl_aff_free(aff);
633 isl_int_set_si(aff->v->el[0], 1);
634 isl_int_set_si(aff->v->el[size], 1);
635
636 return aff;
637 }
638
639 /* Compute
640 *
641 * aff mod m = aff - m * floor(aff/m)
642 */
643 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff, isl_int m)
644 {
645 isl_aff *res;
646
647 res = isl_aff_copy(aff);
648 aff = isl_aff_scale_down(aff, m);
649 aff = isl_aff_floor(aff);
650 aff = isl_aff_scale(aff, m);
651 res = isl_aff_sub(res, aff);
652
653 return res;
654 }
655
656 /* Compute
657 *
658 * pwaff mod m = pwaff - m * floor(pwaff/m)
659 */
660 __isl_give isl_pw_aff *isl_pw_aff_mod(__isl_take isl_pw_aff *pwaff, isl_int m)
661 {
662 isl_pw_aff *res;
663
664 res = isl_pw_aff_copy(pwaff);
665 pwaff = isl_pw_aff_scale_down(pwaff, m);
666 pwaff = isl_pw_aff_floor(pwaff);
667 pwaff = isl_pw_aff_scale(pwaff, m);
668 res = isl_pw_aff_sub(res, pwaff);
669
670 return res;
671 }
672
673 /* Given f, return ceil(f).
674 * If f is an integer expression, then just return f.
675 * Otherwise, create a new div d = [-f] and return the expression -d.
676 */
677 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff)
678 {
679 if (!aff)
680 return NULL;
681
682 if (isl_int_is_one(aff->v->el[0]))
683 return aff;
684
685 aff = isl_aff_neg(aff);
686 aff = isl_aff_floor(aff);
687 aff = isl_aff_neg(aff);
688
689 return aff;
690 }
691
692 /* Apply the expansion computed by isl_merge_divs.
693 * The expansion itself is given by "exp" while the resulting
694 * list of divs is given by "div".
695 */
696 __isl_give isl_aff *isl_aff_expand_divs( __isl_take isl_aff *aff,
697 __isl_take isl_mat *div, int *exp)
698 {
699 int i, j;
700 int old_n_div;
701 int new_n_div;
702 int offset;
703
704 aff = isl_aff_cow(aff);
705 if (!aff || !div)
706 goto error;
707
708 old_n_div = isl_local_space_dim(aff->ls, isl_dim_div);
709 new_n_div = isl_mat_rows(div);
710 if (new_n_div < old_n_div)
711 isl_die(isl_mat_get_ctx(div), isl_error_invalid,
712 "not an expansion", goto error);
713
714 aff->v = isl_vec_extend(aff->v, aff->v->size + new_n_div - old_n_div);
715 if (!aff->v)
716 goto error;
717
718 offset = 1 + isl_local_space_offset(aff->ls, isl_dim_div);
719 j = old_n_div - 1;
720 for (i = new_n_div - 1; i >= 0; --i) {
721 if (j >= 0 && exp[j] == i) {
722 if (i != j)
723 isl_int_swap(aff->v->el[offset + i],
724 aff->v->el[offset + j]);
725 j--;
726 } else
727 isl_int_set_si(aff->v->el[offset + i], 0);
728 }
729
730 aff->ls = isl_local_space_replace_divs(aff->ls, isl_mat_copy(div));
731 if (!aff->ls)
732 goto error;
733 isl_mat_free(div);
734 return aff;
735 error:
736 isl_aff_free(aff);
737 isl_mat_free(div);
738 return NULL;
739 }
740
741 /* Add two affine expressions that live in the same local space.
742 */
743 static __isl_give isl_aff *add_expanded(__isl_take isl_aff *aff1,
744 __isl_take isl_aff *aff2)
745 {
746 isl_int gcd, f;
747
748 aff1 = isl_aff_cow(aff1);
749 if (!aff1 || !aff2)
750 goto error;
751
752 aff1->v = isl_vec_cow(aff1->v);
753 if (!aff1->v)
754 goto error;
755
756 isl_int_init(gcd);
757 isl_int_init(f);
758 isl_int_gcd(gcd, aff1->v->el[0], aff2->v->el[0]);
759 isl_int_divexact(f, aff2->v->el[0], gcd);
760 isl_seq_scale(aff1->v->el + 1, aff1->v->el + 1, f, aff1->v->size - 1);
761 isl_int_divexact(f, aff1->v->el[0], gcd);
762 isl_seq_addmul(aff1->v->el + 1, f, aff2->v->el + 1, aff1->v->size - 1);
763 isl_int_divexact(f, aff2->v->el[0], gcd);
764 isl_int_mul(aff1->v->el[0], aff1->v->el[0], f);
765 isl_int_clear(f);
766 isl_int_clear(gcd);
767
768 isl_aff_free(aff2);
769 return aff1;
770 error:
771 isl_aff_free(aff1);
772 isl_aff_free(aff2);
773 return NULL;
774 }
775
776 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
777 __isl_take isl_aff *aff2)
778 {
779 isl_ctx *ctx;
780 int *exp1 = NULL;
781 int *exp2 = NULL;
782 isl_mat *div;
783
784 if (!aff1 || !aff2)
785 goto error;
786
787 ctx = isl_aff_get_ctx(aff1);
788 if (!isl_space_is_equal(aff1->ls->dim, aff2->ls->dim))
789 isl_die(ctx, isl_error_invalid,
790 "spaces don't match", goto error);
791
792 if (aff1->ls->div->n_row == 0 && aff2->ls->div->n_row == 0)
793 return add_expanded(aff1, aff2);
794
795 exp1 = isl_alloc_array(ctx, int, aff1->ls->div->n_row);
796 exp2 = isl_alloc_array(ctx, int, aff2->ls->div->n_row);
797 if (!exp1 || !exp2)
798 goto error;
799
800 div = isl_merge_divs(aff1->ls->div, aff2->ls->div, exp1, exp2);
801 aff1 = isl_aff_expand_divs(aff1, isl_mat_copy(div), exp1);
802 aff2 = isl_aff_expand_divs(aff2, div, exp2);
803 free(exp1);
804 free(exp2);
805
806 return add_expanded(aff1, aff2);
807 error:
808 free(exp1);
809 free(exp2);
810 isl_aff_free(aff1);
811 isl_aff_free(aff2);
812 return NULL;
813 }
814
815 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
816 __isl_take isl_aff *aff2)
817 {
818 return isl_aff_add(aff1, isl_aff_neg(aff2));
819 }
820
821 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff, isl_int f)
822 {
823 isl_int gcd;
824
825 if (isl_int_is_one(f))
826 return aff;
827
828 aff = isl_aff_cow(aff);
829 if (!aff)
830 return NULL;
831 aff->v = isl_vec_cow(aff->v);
832 if (!aff->v)
833 return isl_aff_free(aff);
834
835 isl_int_init(gcd);
836 isl_int_gcd(gcd, aff->v->el[0], f);
837 isl_int_divexact(aff->v->el[0], aff->v->el[0], gcd);
838 isl_int_divexact(gcd, f, gcd);
839 isl_seq_scale(aff->v->el + 1, aff->v->el + 1, gcd, aff->v->size - 1);
840 isl_int_clear(gcd);
841
842 return aff;
843 }
844
845 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff, isl_int f)
846 {
847 isl_int gcd;
848
849 if (isl_int_is_one(f))
850 return aff;
851
852 aff = isl_aff_cow(aff);
853 if (!aff)
854 return NULL;
855 aff->v = isl_vec_cow(aff->v);
856 if (!aff->v)
857 return isl_aff_free(aff);
858
859 isl_int_init(gcd);
860 isl_seq_gcd(aff->v->el + 1, aff->v->size - 1, &gcd);
861 isl_int_gcd(gcd, gcd, f);
862 isl_seq_scale_down(aff->v->el + 1, aff->v->el + 1, gcd, aff->v->size - 1);
863 isl_int_divexact(gcd, f, gcd);
864 isl_int_mul(aff->v->el[0], aff->v->el[0], gcd);
865 isl_int_clear(gcd);
866
867 return aff;
868 }
869
870 __isl_give isl_aff *isl_aff_scale_down_ui(__isl_take isl_aff *aff, unsigned f)
871 {
872 isl_int v;
873
874 if (f == 1)
875 return aff;
876
877 isl_int_init(v);
878 isl_int_set_ui(v, f);
879 aff = isl_aff_scale_down(aff, v);
880 isl_int_clear(v);
881
882 return aff;
883 }
884
885 __isl_give isl_aff *isl_aff_set_dim_name(__isl_take isl_aff *aff,
886 enum isl_dim_type type, unsigned pos, const char *s)
887 {
888 aff = isl_aff_cow(aff);
889 if (!aff)
890 return NULL;
891 if (type == isl_dim_out)
892 isl_die(aff->v->ctx, isl_error_invalid,
893 "cannot set name of output/set dimension",
894 return isl_aff_free(aff));
895 if (type == isl_dim_in)
896 type = isl_dim_set;
897 aff->ls = isl_local_space_set_dim_name(aff->ls, type, pos, s);
898 if (!aff->ls)
899 return isl_aff_free(aff);
900
901 return aff;
902 }
903
904 __isl_give isl_aff *isl_aff_set_dim_id(__isl_take isl_aff *aff,
905 enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)
906 {
907 aff = isl_aff_cow(aff);
908 if (!aff)
909 return isl_id_free(id);
910 if (type == isl_dim_out)
911 isl_die(aff->v->ctx, isl_error_invalid,
912 "cannot set name of output/set dimension",
913 goto error);
914 if (type == isl_dim_in)
915 type = isl_dim_set;
916 aff->ls = isl_local_space_set_dim_id(aff->ls, type, pos, id);
917 if (!aff->ls)
918 return isl_aff_free(aff);
919
920 return aff;
921 error:
922 isl_id_free(id);
923 isl_aff_free(aff);
924 return NULL;
925 }
926
927 /* Exploit the equalities in "eq" to simplify the affine expression
928 * and the expressions of the integer divisions in the local space.
929 * The integer divisions in this local space are assumed to appear
930 * as regular dimensions in "eq".
931 */
932 static __isl_give isl_aff *isl_aff_substitute_equalities_lifted(
933 __isl_take isl_aff *aff, __isl_take isl_basic_set *eq)
934 {
935 int i, j;
936 unsigned total;
937 unsigned n_div;
938
939 if (!eq)
940 goto error;
941 if (eq->n_eq == 0) {
942 isl_basic_set_free(eq);
943 return aff;
944 }
945
946 aff = isl_aff_cow(aff);
947 if (!aff)
948 goto error;
949
950 aff->ls = isl_local_space_substitute_equalities(aff->ls,
951 isl_basic_set_copy(eq));
952 if (!aff->ls)
953 goto error;
954
955 total = 1 + isl_space_dim(eq->dim, isl_dim_all);
956 n_div = eq->n_div;
957 for (i = 0; i < eq->n_eq; ++i) {
958 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
959 if (j < 0 || j == 0 || j >= total)
960 continue;
961
962 isl_seq_elim(aff->v->el + 1, eq->eq[i], j, total,
963 &aff->v->el[0]);
964 }
965
966 isl_basic_set_free(eq);
967 aff = isl_aff_normalize(aff);
968 return aff;
969 error:
970 isl_basic_set_free(eq);
971 isl_aff_free(aff);
972 return NULL;
973 }
974
975 /* Exploit the equalities in "eq" to simplify the affine expression
976 * and the expressions of the integer divisions in the local space.
977 */
978 static __isl_give isl_aff *isl_aff_substitute_equalities(
979 __isl_take isl_aff *aff, __isl_take isl_basic_set *eq)
980 {
981 int n_div;
982
983 if (!aff || !eq)
984 goto error;
985 n_div = isl_local_space_dim(aff->ls, isl_dim_div);
986 if (n_div > 0)
987 eq = isl_basic_set_add(eq, isl_dim_set, n_div);
988 return isl_aff_substitute_equalities_lifted(aff, eq);
989 error:
990 isl_basic_set_free(eq);
991 isl_aff_free(aff);
992 return NULL;
993 }
994
995 /* Look for equalities among the variables shared by context and aff
996 * and the integer divisions of aff, if any.
997 * The equalities are then used to eliminate coefficients and/or integer
998 * divisions from aff.
999 */
1000 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
1001 __isl_take isl_set *context)
1002 {
1003 isl_basic_set *hull;
1004 int n_div;
1005
1006 if (!aff)
1007 goto error;
1008 n_div = isl_local_space_dim(aff->ls, isl_dim_div);
1009 if (n_div > 0) {
1010 isl_basic_set *bset;
1011 isl_local_space *ls;
1012 context = isl_set_add_dims(context, isl_dim_set, n_div);
1013 ls = isl_aff_get_domain_local_space(aff);
1014 bset = isl_basic_set_from_local_space(ls);
1015 bset = isl_basic_set_lift(bset);
1016 bset = isl_basic_set_flatten(bset);
1017 context = isl_set_intersect(context,
1018 isl_set_from_basic_set(bset));
1019 }
1020
1021 hull = isl_set_affine_hull(context);
1022 return isl_aff_substitute_equalities_lifted(aff, hull);
1023 error:
1024 isl_aff_free(aff);
1025 isl_set_free(context);
1026 return NULL;
1027 }
1028
1029 __isl_give isl_aff *isl_aff_gist_params(__isl_take isl_aff *aff,
1030 __isl_take isl_set *context)
1031 {
1032 isl_set *dom_context = isl_set_universe(isl_aff_get_domain_space(aff));
1033 dom_context = isl_set_intersect_params(dom_context, context);
1034 return isl_aff_gist(aff, dom_context);
1035 }
1036
1037 /* Return a basic set containing those elements in the space
1038 * of aff where it is non-negative.
1039 */
1040 __isl_give isl_basic_set *isl_aff_nonneg_basic_set(__isl_take isl_aff *aff)
1041 {
1042 isl_constraint *ineq;
1043 isl_basic_set *bset;
1044
1045 ineq = isl_inequality_from_aff(aff);
1046
1047 bset = isl_basic_set_from_constraint(ineq);
1048 bset = isl_basic_set_simplify(bset);
1049 return bset;
1050 }
1051
1052 /* Return a basic set containing those elements in the space
1053 * of aff where it is zero.
1054 */
1055 __isl_give isl_basic_set *isl_aff_zero_basic_set(__isl_take isl_aff *aff)
1056 {
1057 isl_constraint *ineq;
1058 isl_basic_set *bset;
1059
1060 ineq = isl_equality_from_aff(aff);
1061
1062 bset = isl_basic_set_from_constraint(ineq);
1063 bset = isl_basic_set_simplify(bset);
1064 return bset;
1065 }
1066
1067 /* Return a basic set containing those elements in the shared space
1068 * of aff1 and aff2 where aff1 is greater than or equal to aff2.
1069 */
1070 __isl_give isl_basic_set *isl_aff_ge_basic_set(__isl_take isl_aff *aff1,
1071 __isl_take isl_aff *aff2)
1072 {
1073 aff1 = isl_aff_sub(aff1, aff2);
1074
1075 return isl_aff_nonneg_basic_set(aff1);
1076 }
1077
1078 /* Return a basic set containing those elements in the shared space
1079 * of aff1 and aff2 where aff1 is smaller than or equal to aff2.
1080 */
1081 __isl_give isl_basic_set *isl_aff_le_basic_set(__isl_take isl_aff *aff1,
1082 __isl_take isl_aff *aff2)
1083 {
1084 return isl_aff_ge_basic_set(aff2, aff1);
1085 }
1086
1087 __isl_give isl_aff *isl_aff_add_on_domain(__isl_keep isl_set *dom,
1088 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2)
1089 {
1090 aff1 = isl_aff_add(aff1, aff2);
1091 aff1 = isl_aff_gist(aff1, isl_set_copy(dom));
1092 return aff1;
1093 }
1094
1095 int isl_aff_is_empty(__isl_keep isl_aff *aff)
1096 {
1097 if (!aff)
1098 return -1;
1099
1100 return 0;
1101 }
1102
1103 /* Check whether the given affine expression has non-zero coefficient
1104 * for any dimension in the given range or if any of these dimensions
1105 * appear with non-zero coefficients in any of the integer divisions
1106 * involved in the affine expression.
1107 */
1108 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
1109 enum isl_dim_type type, unsigned first, unsigned n)
1110 {
1111 int i;
1112 isl_ctx *ctx;
1113 int *active = NULL;
1114 int involves = 0;
1115
1116 if (!aff)
1117 return -1;
1118 if (n == 0)
1119 return 0;
1120
1121 ctx = isl_aff_get_ctx(aff);
1122 if (first + n > isl_aff_dim(aff, type))
1123 isl_die(ctx, isl_error_invalid,
1124 "range out of bounds", return -1);
1125
1126 active = isl_local_space_get_active(aff->ls, aff->v->el + 2);
1127 if (!active)
1128 goto error;
1129
1130 first += isl_local_space_offset(aff->ls, type) - 1;
1131 for (i = 0; i < n; ++i)
1132 if (active[first + i]) {
1133 involves = 1;
1134 break;
1135 }
1136
1137 free(active);
1138
1139 return involves;
1140 error:
1141 free(active);
1142 return -1;
1143 }
1144
1145 __isl_give isl_aff *isl_aff_drop_dims(__isl_take isl_aff *aff,
1146 enum isl_dim_type type, unsigned first, unsigned n)
1147 {
1148 isl_ctx *ctx;
1149
1150 if (!aff)
1151 return NULL;
1152 if (type == isl_dim_out)
1153 isl_die(aff->v->ctx, isl_error_invalid,
1154 "cannot drop output/set dimension",
1155 return isl_aff_free(aff));
1156 if (type == isl_dim_in)
1157 type = isl_dim_set;
1158 if (n == 0 && !isl_local_space_is_named_or_nested(aff->ls, type))
1159 return aff;
1160
1161 ctx = isl_aff_get_ctx(aff);
1162 if (first + n > isl_local_space_dim(aff->ls, type))
1163 isl_die(ctx, isl_error_invalid, "range out of bounds",
1164 return isl_aff_free(aff));
1165
1166 aff = isl_aff_cow(aff);
1167 if (!aff)
1168 return NULL;
1169
1170 aff->ls = isl_local_space_drop_dims(aff->ls, type, first, n);
1171 if (!aff->ls)
1172 return isl_aff_free(aff);
1173
1174 first += 1 + isl_local_space_offset(aff->ls, type);
1175 aff->v = isl_vec_drop_els(aff->v, first, n);
1176 if (!aff->v)
1177 return isl_aff_free(aff);
1178
1179 return aff;
1180 }
1181
1182 /* Project the domain of the affine expression onto its parameter space.
1183 * The affine expression may not involve any of the domain dimensions.
1184 */
1185 __isl_give isl_aff *isl_aff_project_domain_on_params(__isl_take isl_aff *aff)
1186 {
1187 isl_space *space;
1188 unsigned n;
1189 int involves;
1190
1191 n = isl_aff_dim(aff, isl_dim_in);
1192 involves = isl_aff_involves_dims(aff, isl_dim_in, 0, n);
1193 if (involves < 0)
1194 return isl_aff_free(aff);
1195 if (involves)
1196 isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
1197 "affine expression involves some of the domain dimensions",
1198 return isl_aff_free(aff));
1199 aff = isl_aff_drop_dims(aff, isl_dim_in, 0, n);
1200 space = isl_aff_get_domain_space(aff);
1201 space = isl_space_params(space);
1202 aff = isl_aff_reset_domain_space(aff, space);
1203 return aff;
1204 }
1205
1206 __isl_give isl_aff *isl_aff_insert_dims(__isl_take isl_aff *aff,
1207 enum isl_dim_type type, unsigned first, unsigned n)
1208 {
1209 isl_ctx *ctx;
1210
1211 if (!aff)
1212 return NULL;
1213 if (type == isl_dim_out)
1214 isl_die(aff->v->ctx, isl_error_invalid,
1215 "cannot insert output/set dimensions",
1216 return isl_aff_free(aff));
1217 if (type == isl_dim_in)
1218 type = isl_dim_set;
1219 if (n == 0 && !isl_local_space_is_named_or_nested(aff->ls, type))
1220 return aff;
1221
1222 ctx = isl_aff_get_ctx(aff);
1223 if (first > isl_local_space_dim(aff->ls, type))
1224 isl_die(ctx, isl_error_invalid, "position out of bounds",
1225 return isl_aff_free(aff));
1226
1227 aff = isl_aff_cow(aff);
1228 if (!aff)
1229 return NULL;
1230
1231 aff->ls = isl_local_space_insert_dims(aff->ls, type, first, n);
1232 if (!aff->ls)
1233 return isl_aff_free(aff);
1234
1235 first += 1 + isl_local_space_offset(aff->ls, type);
1236 aff->v = isl_vec_insert_zero_els(aff->v, first, n);
1237 if (!aff->v)
1238 return isl_aff_free(aff);
1239
1240 return aff;
1241 }
1242
1243 __isl_give isl_aff *isl_aff_add_dims(__isl_take isl_aff *aff,
1244 enum isl_dim_type type, unsigned n)
1245 {
1246 unsigned pos;
1247
1248 pos = isl_aff_dim(aff, type);
1249
1250 return isl_aff_insert_dims(aff, type, pos, n);
1251 }
1252
1253 __isl_give isl_pw_aff *isl_pw_aff_add_dims(__isl_take isl_pw_aff *pwaff,
1254 enum isl_dim_type type, unsigned n)
1255 {
1256 unsigned pos;
1257
1258 pos = isl_pw_aff_dim(pwaff, type);
1259
1260 return isl_pw_aff_insert_dims(pwaff, type, pos, n);
1261 }
1262
1263 __isl_give isl_pw_aff *isl_pw_aff_from_aff(__isl_take isl_aff *aff)
1264 {
1265 isl_set *dom = isl_set_universe(isl_aff_get_domain_space(aff));
1266 return isl_pw_aff_alloc(dom, aff);
1267 }
1268
1269 #undef PW
1270 #define PW isl_pw_aff
1271 #undef EL
1272 #define EL isl_aff
1273 #undef EL_IS_ZERO
1274 #define EL_IS_ZERO is_empty
1275 #undef ZERO
1276 #define ZERO empty
1277 #undef IS_ZERO
1278 #define IS_ZERO is_empty
1279 #undef FIELD
1280 #define FIELD aff
1281 #undef DEFAULT_IS_ZERO
1282 #define DEFAULT_IS_ZERO 0
1283
1284 #define NO_EVAL
1285 #define NO_OPT
1286 #define NO_MOVE_DIMS
1287 #define NO_LIFT
1288 #define NO_MORPH
1289
1290 #include <isl_pw_templ.c>
1291
1292 static __isl_give isl_set *align_params_pw_pw_set_and(
1293 __isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2,
1294 __isl_give isl_set *(*fn)(__isl_take isl_pw_aff *pwaff1,
1295 __isl_take isl_pw_aff *pwaff2))
1296 {
1297 if (!pwaff1 || !pwaff2)
1298 goto error;
1299 if (isl_space_match(pwaff1->dim, isl_dim_param,
1300 pwaff2->dim, isl_dim_param))
1301 return fn(pwaff1, pwaff2);
1302 if (!isl_space_has_named_params(pwaff1->dim) ||
1303 !isl_space_has_named_params(pwaff2->dim))
1304 isl_die(isl_pw_aff_get_ctx(pwaff1), isl_error_invalid,
1305 "unaligned unnamed parameters", goto error);
1306 pwaff1 = isl_pw_aff_align_params(pwaff1, isl_pw_aff_get_space(pwaff2));
1307 pwaff2 = isl_pw_aff_align_params(pwaff2, isl_pw_aff_get_space(pwaff1));
1308 return fn(pwaff1, pwaff2);
1309 error:
1310 isl_pw_aff_free(pwaff1);
1311 isl_pw_aff_free(pwaff2);
1312 return NULL;
1313 }
1314
1315 /* Compute a piecewise quasi-affine expression with a domain that
1316 * is the union of those of pwaff1 and pwaff2 and such that on each
1317 * cell, the quasi-affine expression is the better (according to cmp)
1318 * of those of pwaff1 and pwaff2. If only one of pwaff1 or pwaff2
1319 * is defined on a given cell, then the associated expression
1320 * is the defined one.
1321 */
1322 static __isl_give isl_pw_aff *pw_aff_union_opt(__isl_take isl_pw_aff *pwaff1,
1323 __isl_take isl_pw_aff *pwaff2,
1324 __isl_give isl_basic_set *(*cmp)(__isl_take isl_aff *aff1,
1325 __isl_take isl_aff *aff2))
1326 {
1327 int i, j, n;
1328 isl_pw_aff *res;
1329 isl_ctx *ctx;
1330 isl_set *set;
1331
1332 if (!pwaff1 || !pwaff2)
1333 goto error;
1334
1335 ctx = isl_space_get_ctx(pwaff1->dim);
1336 if (!isl_space_is_equal(pwaff1->dim, pwaff2->dim))
1337 isl_die(ctx, isl_error_invalid,
1338 "arguments should live in same space", goto error);
1339
1340 if (isl_pw_aff_is_empty(pwaff1)) {
1341 isl_pw_aff_free(pwaff1);
1342 return pwaff2;
1343 }
1344
1345 if (isl_pw_aff_is_empty(pwaff2)) {
1346 isl_pw_aff_free(pwaff2);
1347 return pwaff1;
1348 }
1349
1350 n = 2 * (pwaff1->n + 1) * (pwaff2->n + 1);
1351 res = isl_pw_aff_alloc_size(isl_space_copy(pwaff1->dim), n);
1352
1353 for (i = 0; i < pwaff1->n; ++i) {
1354 set = isl_set_copy(pwaff1->p[i].set);
1355 for (j = 0; j < pwaff2->n; ++j) {
1356 struct isl_set *common;
1357 isl_set *better;
1358
1359 common = isl_set_intersect(
1360 isl_set_copy(pwaff1->p[i].set),
1361 isl_set_copy(pwaff2->p[j].set));
1362 better = isl_set_from_basic_set(cmp(
1363 isl_aff_copy(pwaff2->p[j].aff),
1364 isl_aff_copy(pwaff1->p[i].aff)));
1365 better = isl_set_intersect(common, better);
1366 if (isl_set_plain_is_empty(better)) {
1367 isl_set_free(better);
1368 continue;
1369 }
1370 set = isl_set_subtract(set, isl_set_copy(better));
1371
1372 res = isl_pw_aff_add_piece(res, better,
1373 isl_aff_copy(pwaff2->p[j].aff));
1374 }
1375 res = isl_pw_aff_add_piece(res, set,
1376 isl_aff_copy(pwaff1->p[i].aff));
1377 }
1378
1379 for (j = 0; j < pwaff2->n; ++j) {
1380 set = isl_set_copy(pwaff2->p[j].set);
1381 for (i = 0; i < pwaff1->n; ++i)
1382 set = isl_set_subtract(set,
1383 isl_set_copy(pwaff1->p[i].set));
1384 res = isl_pw_aff_add_piece(res, set,
1385 isl_aff_copy(pwaff2->p[j].aff));
1386 }
1387
1388 isl_pw_aff_free(pwaff1);
1389 isl_pw_aff_free(pwaff2);
1390
1391 return res;
1392 error:
1393 isl_pw_aff_free(pwaff1);
1394 isl_pw_aff_free(pwaff2);
1395 return NULL;
1396 }
1397
1398 /* Compute a piecewise quasi-affine expression with a domain that
1399 * is the union of those of pwaff1 and pwaff2 and such that on each
1400 * cell, the quasi-affine expression is the maximum of those of pwaff1
1401 * and pwaff2. If only one of pwaff1 or pwaff2 is defined on a given
1402 * cell, then the associated expression is the defined one.
1403 */
1404 static __isl_give isl_pw_aff *pw_aff_union_max(__isl_take isl_pw_aff *pwaff1,
1405 __isl_take isl_pw_aff *pwaff2)
1406 {
1407 return pw_aff_union_opt(pwaff1, pwaff2, &isl_aff_ge_basic_set);
1408 }
1409
1410 __isl_give isl_pw_aff *isl_pw_aff_union_max(__isl_take isl_pw_aff *pwaff1,
1411 __isl_take isl_pw_aff *pwaff2)
1412 {
1413 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2,
1414 &pw_aff_union_max);
1415 }
1416
1417 /* Compute a piecewise quasi-affine expression with a domain that
1418 * is the union of those of pwaff1 and pwaff2 and such that on each
1419 * cell, the quasi-affine expression is the minimum of those of pwaff1
1420 * and pwaff2. If only one of pwaff1 or pwaff2 is defined on a given
1421 * cell, then the associated expression is the defined one.
1422 */
1423 static __isl_give isl_pw_aff *pw_aff_union_min(__isl_take isl_pw_aff *pwaff1,
1424 __isl_take isl_pw_aff *pwaff2)
1425 {
1426 return pw_aff_union_opt(pwaff1, pwaff2, &isl_aff_le_basic_set);
1427 }
1428
1429 __isl_give isl_pw_aff *isl_pw_aff_union_min(__isl_take isl_pw_aff *pwaff1,
1430 __isl_take isl_pw_aff *pwaff2)
1431 {
1432 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2,
1433 &pw_aff_union_min);
1434 }
1435
1436 __isl_give isl_pw_aff *isl_pw_aff_union_opt(__isl_take isl_pw_aff *pwaff1,
1437 __isl_take isl_pw_aff *pwaff2, int max)
1438 {
1439 if (max)
1440 return isl_pw_aff_union_max(pwaff1, pwaff2);
1441 else
1442 return isl_pw_aff_union_min(pwaff1, pwaff2);
1443 }
1444
1445 /* Construct a map with as domain the domain of pwaff and
1446 * one-dimensional range corresponding to the affine expressions.
1447 */
1448 static __isl_give isl_map *map_from_pw_aff(__isl_take isl_pw_aff *pwaff)
1449 {
1450 int i;
1451 isl_space *dim;
1452 isl_map *map;
1453
1454 if (!pwaff)
1455 return NULL;
1456
1457 dim = isl_pw_aff_get_space(pwaff);
1458 map = isl_map_empty(dim);
1459
1460 for (i = 0; i < pwaff->n; ++i) {
1461 isl_basic_map *bmap;
1462 isl_map *map_i;
1463
1464 bmap = isl_basic_map_from_aff(isl_aff_copy(pwaff->p[i].aff));
1465 map_i = isl_map_from_basic_map(bmap);
1466 map_i = isl_map_intersect_domain(map_i,
1467 isl_set_copy(pwaff->p[i].set));
1468 map = isl_map_union_disjoint(map, map_i);
1469 }
1470
1471 isl_pw_aff_free(pwaff);
1472
1473 return map;
1474 }
1475
1476 /* Construct a map with as domain the domain of pwaff and
1477 * one-dimensional range corresponding to the affine expressions.
1478 */
1479 __isl_give isl_map *isl_map_from_pw_aff(__isl_take isl_pw_aff *pwaff)
1480 {
1481 if (!pwaff)
1482 return NULL;
1483 if (isl_space_is_set(pwaff->dim))
1484 isl_die(isl_pw_aff_get_ctx(pwaff), isl_error_invalid,
1485 "space of input is not a map",
1486 return isl_pw_aff_free(pwaff));
1487 return map_from_pw_aff(pwaff);
1488 }
1489
1490 /* Construct a one-dimensional set with as parameter domain
1491 * the domain of pwaff and the single set dimension
1492 * corresponding to the affine expressions.
1493 */
1494 __isl_give isl_set *isl_set_from_pw_aff(__isl_take isl_pw_aff *pwaff)
1495 {
1496 if (!pwaff)
1497 return NULL;
1498 if (!isl_space_is_set(pwaff->dim))
1499 isl_die(isl_pw_aff_get_ctx(pwaff), isl_error_invalid,
1500 "space of input is not a set",
1501 return isl_pw_aff_free(pwaff));
1502 return map_from_pw_aff(pwaff);
1503 }
1504
1505 /* Return a set containing those elements in the domain
1506 * of pwaff where it is non-negative.
1507 */
1508 __isl_give isl_set *isl_pw_aff_nonneg_set(__isl_take isl_pw_aff *pwaff)
1509 {
1510 int i;
1511 isl_set *set;
1512
1513 if (!pwaff)
1514 return NULL;
1515
1516 set = isl_set_empty(isl_pw_aff_get_domain_space(pwaff));
1517
1518 for (i = 0; i < pwaff->n; ++i) {
1519 isl_basic_set *bset;
1520 isl_set *set_i;
1521
1522 bset = isl_aff_nonneg_basic_set(isl_aff_copy(pwaff->p[i].aff));
1523 set_i = isl_set_from_basic_set(bset);
1524 set_i = isl_set_intersect(set_i, isl_set_copy(pwaff->p[i].set));
1525 set = isl_set_union_disjoint(set, set_i);
1526 }
1527
1528 isl_pw_aff_free(pwaff);
1529
1530 return set;
1531 }
1532
1533 /* Return a set containing those elements in the domain
1534 * of pwaff where it is zero (if complement is 0) or not zero
1535 * (if complement is 1).
1536 */
1537 static __isl_give isl_set *pw_aff_zero_set(__isl_take isl_pw_aff *pwaff,
1538 int complement)
1539 {
1540 int i;
1541 isl_set *set;
1542
1543 if (!pwaff)
1544 return NULL;
1545
1546 set = isl_set_empty(isl_pw_aff_get_domain_space(pwaff));
1547
1548 for (i = 0; i < pwaff->n; ++i) {
1549 isl_basic_set *bset;
1550 isl_set *set_i, *zero;
1551
1552 bset = isl_aff_zero_basic_set(isl_aff_copy(pwaff->p[i].aff));
1553 zero = isl_set_from_basic_set(bset);
1554 set_i = isl_set_copy(pwaff->p[i].set);
1555 if (complement)
1556 set_i = isl_set_subtract(set_i, zero);
1557 else
1558 set_i = isl_set_intersect(set_i, zero);
1559 set = isl_set_union_disjoint(set, set_i);
1560 }
1561
1562 isl_pw_aff_free(pwaff);
1563
1564 return set;
1565 }
1566
1567 /* Return a set containing those elements in the domain
1568 * of pwaff where it is zero.
1569 */
1570 __isl_give isl_set *isl_pw_aff_zero_set(__isl_take isl_pw_aff *pwaff)
1571 {
1572 return pw_aff_zero_set(pwaff, 0);
1573 }
1574
1575 /* Return a set containing those elements in the domain
1576 * of pwaff where it is not zero.
1577 */
1578 __isl_give isl_set *isl_pw_aff_non_zero_set(__isl_take isl_pw_aff *pwaff)
1579 {
1580 return pw_aff_zero_set(pwaff, 1);
1581 }
1582
1583 /* Return a set containing those elements in the shared domain
1584 * of pwaff1 and pwaff2 where pwaff1 is greater than (or equal) to pwaff2.
1585 *
1586 * We compute the difference on the shared domain and then construct
1587 * the set of values where this difference is non-negative.
1588 * If strict is set, we first subtract 1 from the difference.
1589 * If equal is set, we only return the elements where pwaff1 and pwaff2
1590 * are equal.
1591 */
1592 static __isl_give isl_set *pw_aff_gte_set(__isl_take isl_pw_aff *pwaff1,
1593 __isl_take isl_pw_aff *pwaff2, int strict, int equal)
1594 {
1595 isl_set *set1, *set2;
1596
1597 set1 = isl_pw_aff_domain(isl_pw_aff_copy(pwaff1));
1598 set2 = isl_pw_aff_domain(isl_pw_aff_copy(pwaff2));
1599 set1 = isl_set_intersect(set1, set2);
1600 pwaff1 = isl_pw_aff_intersect_domain(pwaff1, isl_set_copy(set1));
1601 pwaff2 = isl_pw_aff_intersect_domain(pwaff2, isl_set_copy(set1));
1602 pwaff1 = isl_pw_aff_add(pwaff1, isl_pw_aff_neg(pwaff2));
1603
1604 if (strict) {
1605 isl_space *dim = isl_set_get_space(set1);
1606 isl_aff *aff;
1607 aff = isl_aff_zero_on_domain(isl_local_space_from_space(dim));
1608 aff = isl_aff_add_constant_si(aff, -1);
1609 pwaff1 = isl_pw_aff_add(pwaff1, isl_pw_aff_alloc(set1, aff));
1610 } else
1611 isl_set_free(set1);
1612
1613 if (equal)
1614 return isl_pw_aff_zero_set(pwaff1);
1615 return isl_pw_aff_nonneg_set(pwaff1);
1616 }
1617
1618 /* Return a set containing those elements in the shared domain
1619 * of pwaff1 and pwaff2 where pwaff1 is equal to pwaff2.
1620 */
1621 static __isl_give isl_set *pw_aff_eq_set(__isl_take isl_pw_aff *pwaff1,
1622 __isl_take isl_pw_aff *pwaff2)
1623 {
1624 return pw_aff_gte_set(pwaff1, pwaff2, 0, 1);
1625 }
1626
1627 __isl_give isl_set *isl_pw_aff_eq_set(__isl_take isl_pw_aff *pwaff1,
1628 __isl_take isl_pw_aff *pwaff2)
1629 {
1630 return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_eq_set);
1631 }
1632
1633 /* Return a set containing those elements in the shared domain
1634 * of pwaff1 and pwaff2 where pwaff1 is greater than or equal to pwaff2.
1635 */
1636 static __isl_give isl_set *pw_aff_ge_set(__isl_take isl_pw_aff *pwaff1,
1637 __isl_take isl_pw_aff *pwaff2)
1638 {
1639 return pw_aff_gte_set(pwaff1, pwaff2, 0, 0);
1640 }
1641
1642 __isl_give isl_set *isl_pw_aff_ge_set(__isl_take isl_pw_aff *pwaff1,
1643 __isl_take isl_pw_aff *pwaff2)
1644 {
1645 return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_ge_set);
1646 }
1647
1648 /* Return a set containing those elements in the shared domain
1649 * of pwaff1 and pwaff2 where pwaff1 is strictly greater than pwaff2.
1650 */
1651 static __isl_give isl_set *pw_aff_gt_set(__isl_take isl_pw_aff *pwaff1,
1652 __isl_take isl_pw_aff *pwaff2)
1653 {
1654 return pw_aff_gte_set(pwaff1, pwaff2, 1, 0);
1655 }
1656
1657 __isl_give isl_set *isl_pw_aff_gt_set(__isl_take isl_pw_aff *pwaff1,
1658 __isl_take isl_pw_aff *pwaff2)
1659 {
1660 return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_gt_set);
1661 }
1662
1663 __isl_give isl_set *isl_pw_aff_le_set(__isl_take isl_pw_aff *pwaff1,
1664 __isl_take isl_pw_aff *pwaff2)
1665 {
1666 return isl_pw_aff_ge_set(pwaff2, pwaff1);
1667 }
1668
1669 __isl_give isl_set *isl_pw_aff_lt_set(__isl_take isl_pw_aff *pwaff1,
1670 __isl_take isl_pw_aff *pwaff2)
1671 {
1672 return isl_pw_aff_gt_set(pwaff2, pwaff1);
1673 }
1674
1675 /* Return a set containing those elements in the shared domain
1676 * of the elements of list1 and list2 where each element in list1
1677 * has the relation specified by "fn" with each element in list2.
1678 */
1679 static __isl_give isl_set *pw_aff_list_set(__isl_take isl_pw_aff_list *list1,
1680 __isl_take isl_pw_aff_list *list2,
1681 __isl_give isl_set *(*fn)(__isl_take isl_pw_aff *pwaff1,
1682 __isl_take isl_pw_aff *pwaff2))
1683 {
1684 int i, j;
1685 isl_ctx *ctx;
1686 isl_set *set;
1687
1688 if (!list1 || !list2)
1689 goto error;
1690
1691 ctx = isl_pw_aff_list_get_ctx(list1);
1692 if (list1->n < 1 || list2->n < 1)
1693 isl_die(ctx, isl_error_invalid,
1694 "list should contain at least one element", goto error);
1695
1696 set = isl_set_universe(isl_pw_aff_get_domain_space(list1->p[0]));
1697 for (i = 0; i < list1->n; ++i)
1698 for (j = 0; j < list2->n; ++j) {
1699 isl_set *set_ij;
1700
1701 set_ij = fn(isl_pw_aff_copy(list1->p[i]),
1702 isl_pw_aff_copy(list2->p[j]));
1703 set = isl_set_intersect(set, set_ij);
1704 }
1705
1706 isl_pw_aff_list_free(list1);
1707 isl_pw_aff_list_free(list2);
1708 return set;
1709 error:
1710 isl_pw_aff_list_free(list1);
1711 isl_pw_aff_list_free(list2);
1712 return NULL;
1713 }
1714
1715 /* Return a set containing those elements in the shared domain
1716 * of the elements of list1 and list2 where each element in list1
1717 * is equal to each element in list2.
1718 */
1719 __isl_give isl_set *isl_pw_aff_list_eq_set(__isl_take isl_pw_aff_list *list1,
1720 __isl_take isl_pw_aff_list *list2)
1721 {
1722 return pw_aff_list_set(list1, list2, &isl_pw_aff_eq_set);
1723 }
1724
1725 __isl_give isl_set *isl_pw_aff_list_ne_set(__isl_take isl_pw_aff_list *list1,
1726 __isl_take isl_pw_aff_list *list2)
1727 {
1728 return pw_aff_list_set(list1, list2, &isl_pw_aff_ne_set);
1729 }
1730
1731 /* Return a set containing those elements in the shared domain
1732 * of the elements of list1 and list2 where each element in list1
1733 * is less than or equal to each element in list2.
1734 */
1735 __isl_give isl_set *isl_pw_aff_list_le_set(__isl_take isl_pw_aff_list *list1,
1736 __isl_take isl_pw_aff_list *list2)
1737 {
1738 return pw_aff_list_set(list1, list2, &isl_pw_aff_le_set);
1739 }
1740
1741 __isl_give isl_set *isl_pw_aff_list_lt_set(__isl_take isl_pw_aff_list *list1,
1742 __isl_take isl_pw_aff_list *list2)
1743 {
1744 return pw_aff_list_set(list1, list2, &isl_pw_aff_lt_set);
1745 }
1746
1747 __isl_give isl_set *isl_pw_aff_list_ge_set(__isl_take isl_pw_aff_list *list1,
1748 __isl_take isl_pw_aff_list *list2)
1749 {
1750 return pw_aff_list_set(list1, list2, &isl_pw_aff_ge_set);
1751 }
1752
1753 __isl_give isl_set *isl_pw_aff_list_gt_set(__isl_take isl_pw_aff_list *list1,
1754 __isl_take isl_pw_aff_list *list2)
1755 {
1756 return pw_aff_list_set(list1, list2, &isl_pw_aff_gt_set);
1757 }
1758
1759
1760 /* Return a set containing those elements in the shared domain
1761 * of pwaff1 and pwaff2 where pwaff1 is not equal to pwaff2.
1762 */
1763 static __isl_give isl_set *pw_aff_ne_set(__isl_take isl_pw_aff *pwaff1,
1764 __isl_take isl_pw_aff *pwaff2)
1765 {
1766 isl_set *set_lt, *set_gt;
1767
1768 set_lt = isl_pw_aff_lt_set(isl_pw_aff_copy(pwaff1),
1769 isl_pw_aff_copy(pwaff2));
1770 set_gt = isl_pw_aff_gt_set(pwaff1, pwaff2);
1771 return isl_set_union_disjoint(set_lt, set_gt);
1772 }
1773
1774 __isl_give isl_set *isl_pw_aff_ne_set(__isl_take isl_pw_aff *pwaff1,
1775 __isl_take isl_pw_aff *pwaff2)
1776 {
1777 return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_ne_set);
1778 }
1779
1780 __isl_give isl_pw_aff *isl_pw_aff_scale_down(__isl_take isl_pw_aff *pwaff,
1781 isl_int v)
1782 {
1783 int i;
1784
1785 if (isl_int_is_one(v))
1786 return pwaff;
1787 if (!isl_int_is_pos(v))
1788 isl_die(isl_pw_aff_get_ctx(pwaff), isl_error_invalid,
1789 "factor needs to be positive",
1790 return isl_pw_aff_free(pwaff));
1791 pwaff = isl_pw_aff_cow(pwaff);
1792 if (!pwaff)
1793 return NULL;
1794 if (pwaff->n == 0)
1795 return pwaff;
1796
1797 for (i = 0; i < pwaff->n; ++i) {
1798 pwaff->p[i].aff = isl_aff_scale_down(pwaff->p[i].aff, v);
1799 if (!pwaff->p[i].aff)
1800 return isl_pw_aff_free(pwaff);
1801 }
1802
1803 return pwaff;
1804 }
1805
1806 __isl_give isl_pw_aff *isl_pw_aff_floor(__isl_take isl_pw_aff *pwaff)
1807 {
1808 int i;
1809
1810 pwaff = isl_pw_aff_cow(pwaff);
1811 if (!pwaff)
1812 return NULL;
1813 if (pwaff->n == 0)
1814 return pwaff;
1815
1816 for (i = 0; i < pwaff->n; ++i) {
1817 pwaff->p[i].aff = isl_aff_floor(pwaff->p[i].aff);
1818 if (!pwaff->p[i].aff)
1819 return isl_pw_aff_free(pwaff);
1820 }
1821
1822 return pwaff;
1823 }
1824
1825 __isl_give isl_pw_aff *isl_pw_aff_ceil(__isl_take isl_pw_aff *pwaff)
1826 {
1827 int i;
1828
1829 pwaff = isl_pw_aff_cow(pwaff);
1830 if (!pwaff)
1831 return NULL;
1832 if (pwaff->n == 0)
1833 return pwaff;
1834
1835 for (i = 0; i < pwaff->n; ++i) {
1836 pwaff->p[i].aff = isl_aff_ceil(pwaff->p[i].aff);
1837 if (!pwaff->p[i].aff)
1838 return isl_pw_aff_free(pwaff);
1839 }
1840
1841 return pwaff;
1842 }
1843
1844 /* Return an affine expression that is equal to pwaff_true for elements
1845 * in "cond" and to pwaff_false for elements not in "cond".
1846 * That is, return cond ? pwaff_true : pwaff_false;
1847 */
1848 __isl_give isl_pw_aff *isl_pw_aff_cond(__isl_take isl_set *cond,
1849 __isl_take isl_pw_aff *pwaff_true, __isl_take isl_pw_aff *pwaff_false)
1850 {
1851 isl_set *comp;
1852
1853 comp = isl_set_complement(isl_set_copy(cond));
1854 pwaff_true = isl_pw_aff_intersect_domain(pwaff_true, cond);
1855 pwaff_false = isl_pw_aff_intersect_domain(pwaff_false, comp);
1856
1857 return isl_pw_aff_add_disjoint(pwaff_true, pwaff_false);
1858 }
1859
1860 int isl_aff_is_cst(__isl_keep isl_aff *aff)
1861 {
1862 if (!aff)
1863 return -1;
1864
1865 return isl_seq_first_non_zero(aff->v->el + 2, aff->v->size - 2) == -1;
1866 }
1867
1868 /* Check whether pwaff is a piecewise constant.
1869 */
1870 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff)
1871 {
1872 int i;
1873
1874 if (!pwaff)
1875 return -1;
1876
1877 for (i = 0; i < pwaff->n; ++i) {
1878 int is_cst = isl_aff_is_cst(pwaff->p[i].aff);
1879 if (is_cst < 0 || !is_cst)
1880 return is_cst;
1881 }
1882
1883 return 1;
1884 }
1885
1886 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
1887 __isl_take isl_aff *aff2)
1888 {
1889 if (!isl_aff_is_cst(aff2) && isl_aff_is_cst(aff1))
1890 return isl_aff_mul(aff2, aff1);
1891
1892 if (!isl_aff_is_cst(aff2))
1893 isl_die(isl_aff_get_ctx(aff1), isl_error_invalid,
1894 "at least one affine expression should be constant",
1895 goto error);
1896
1897 aff1 = isl_aff_cow(aff1);
1898 if (!aff1 || !aff2)
1899 goto error;
1900
1901 aff1 = isl_aff_scale(aff1, aff2->v->el[1]);
1902 aff1 = isl_aff_scale_down(aff1, aff2->v->el[0]);
1903
1904 isl_aff_free(aff2);
1905 return aff1;
1906 error:
1907 isl_aff_free(aff1);
1908 isl_aff_free(aff2);
1909 return NULL;
1910 }
1911
1912 static __isl_give isl_pw_aff *pw_aff_add(__isl_take isl_pw_aff *pwaff1,
1913 __isl_take isl_pw_aff *pwaff2)
1914 {
1915 return isl_pw_aff_on_shared_domain(pwaff1, pwaff2, &isl_aff_add);
1916 }
1917
1918 __isl_give isl_pw_aff *isl_pw_aff_add(__isl_take isl_pw_aff *pwaff1,
1919 __isl_take isl_pw_aff *pwaff2)
1920 {
1921 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_add);
1922 }
1923
1924 __isl_give isl_pw_aff *isl_pw_aff_union_add(__isl_take isl_pw_aff *pwaff1,
1925 __isl_take isl_pw_aff *pwaff2)
1926 {
1927 return isl_pw_aff_union_add_(pwaff1, pwaff2);
1928 }
1929
1930 static __isl_give isl_pw_aff *pw_aff_mul(__isl_take isl_pw_aff *pwaff1,
1931 __isl_take isl_pw_aff *pwaff2)
1932 {
1933 return isl_pw_aff_on_shared_domain(pwaff1, pwaff2, &isl_aff_mul);
1934 }
1935
1936 __isl_give isl_pw_aff *isl_pw_aff_mul(__isl_take isl_pw_aff *pwaff1,
1937 __isl_take isl_pw_aff *pwaff2)
1938 {
1939 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_mul);
1940 }
1941
1942 static __isl_give isl_pw_aff *pw_aff_min(__isl_take isl_pw_aff *pwaff1,
1943 __isl_take isl_pw_aff *pwaff2)
1944 {
1945 isl_set *le;
1946
1947 le = isl_pw_aff_le_set(isl_pw_aff_copy(pwaff1),
1948 isl_pw_aff_copy(pwaff2));
1949 return isl_pw_aff_cond(le, pwaff1, pwaff2);
1950 }
1951
1952 __isl_give isl_pw_aff *isl_pw_aff_min(__isl_take isl_pw_aff *pwaff1,
1953 __isl_take isl_pw_aff *pwaff2)
1954 {
1955 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_min);
1956 }
1957
1958 static __isl_give isl_pw_aff *pw_aff_max(__isl_take isl_pw_aff *pwaff1,
1959 __isl_take isl_pw_aff *pwaff2)
1960 {
1961 isl_set *le;
1962
1963 le = isl_pw_aff_ge_set(isl_pw_aff_copy(pwaff1),
1964 isl_pw_aff_copy(pwaff2));
1965 return isl_pw_aff_cond(le, pwaff1, pwaff2);
1966 }
1967
1968 __isl_give isl_pw_aff *isl_pw_aff_max(__isl_take isl_pw_aff *pwaff1,
1969 __isl_take isl_pw_aff *pwaff2)
1970 {
1971 return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_max);
1972 }
1973
1974 static __isl_give isl_pw_aff *pw_aff_list_reduce(
1975 __isl_take isl_pw_aff_list *list,
1976 __isl_give isl_pw_aff *(*fn)(__isl_take isl_pw_aff *pwaff1,
1977 __isl_take isl_pw_aff *pwaff2))
1978 {
1979 int i;
1980 isl_ctx *ctx;
1981 isl_pw_aff *res;
1982
1983 if (!list)
1984 return NULL;
1985
1986 ctx = isl_pw_aff_list_get_ctx(list);
1987 if (list->n < 1)
1988 isl_die(ctx, isl_error_invalid,
1989 "list should contain at least one element",
1990 return isl_pw_aff_list_free(list));
1991
1992 res = isl_pw_aff_copy(list->p[0]);
1993 for (i = 1; i < list->n; ++i)
1994 res = fn(res, isl_pw_aff_copy(list->p[i]));
1995
1996 isl_pw_aff_list_free(list);
1997 return res;
1998 }
1999
2000 /* Return an isl_pw_aff that maps each element in the intersection of the
2001 * domains of the elements of list to the minimal corresponding affine
2002 * expression.
2003 */
2004 __isl_give isl_pw_aff *isl_pw_aff_list_min(__isl_take isl_pw_aff_list *list)
2005 {
2006 return pw_aff_list_reduce(list, &isl_pw_aff_min);
2007 }
2008
2009 /* Return an isl_pw_aff that maps each element in the intersection of the
2010 * domains of the elements of list to the maximal corresponding affine
2011 * expression.
2012 */
2013 __isl_give isl_pw_aff *isl_pw_aff_list_max(__isl_take isl_pw_aff_list *list)
2014 {
2015 return pw_aff_list_reduce(list, &isl_pw_aff_max);
2016 }
2017
2018 #undef BASE
2019 #define BASE aff
2020
2021 #include <isl_multi_templ.c>
2022
2023 __isl_give isl_multi_aff *isl_multi_aff_add(__isl_take isl_multi_aff *maff1,
2024 __isl_take isl_multi_aff *maff2)
2025 {
2026 int i;
2027 isl_ctx *ctx;
2028
2029 maff1 = isl_multi_aff_cow(maff1);
2030 if (!maff1 || !maff2)
2031 goto error;
2032
2033 ctx = isl_multi_aff_get_ctx(maff1);
2034 if (!isl_space_is_equal(maff1->space, maff2->space))
2035 isl_die(ctx, isl_error_invalid,
2036 "spaces don't match", goto error);
2037
2038 for (i = 0; i < maff1->n; ++i) {
2039 maff1->p[i] = isl_aff_add(maff1->p[i],
2040 isl_aff_copy(maff2->p[i]));
2041 if (!maff1->p[i])
2042 goto error;
2043 }
2044
2045 isl_multi_aff_free(maff2);
2046 return maff1;
2047 error:
2048 isl_multi_aff_free(maff1);
2049 isl_multi_aff_free(maff2);
2050 return NULL;
2051 }
2052
2053 /* Exploit the equalities in "eq" to simplify the affine expressions.
2054 */
2055 static __isl_give isl_multi_aff *isl_multi_aff_substitute_equalities(
2056 __isl_take isl_multi_aff *maff, __isl_take isl_basic_set *eq)
2057 {
2058 int i;
2059
2060 maff = isl_multi_aff_cow(maff);
2061 if (!maff || !eq)
2062 goto error;
2063
2064 for (i = 0; i < maff->n; ++i) {
2065 maff->p[i] = isl_aff_substitute_equalities(maff->p[i],
2066 isl_basic_set_copy(eq));
2067 if (!maff->p[i])
2068 goto error;
2069 }
2070
2071 isl_basic_set_free(eq);
2072 return maff;
2073 error:
2074 isl_basic_set_free(eq);
2075 isl_multi_aff_free(maff);
2076 return NULL;
2077 }
2078
2079 __isl_give isl_multi_aff *isl_multi_aff_scale(__isl_take isl_multi_aff *maff,
2080 isl_int f)
2081 {
2082 int i;
2083
2084 maff = isl_multi_aff_cow(maff);
2085 if (!maff)
2086 return NULL;
2087
2088 for (i = 0; i < maff->n; ++i) {
2089 maff->p[i] = isl_aff_scale(maff->p[i], f);
2090 if (!maff->p[i])
2091 return isl_multi_aff_free(maff);
2092 }
2093
2094 return maff;
2095 }
2096
2097 __isl_give isl_multi_aff *isl_multi_aff_add_on_domain(__isl_keep isl_set *dom,
2098 __isl_take isl_multi_aff *maff1, __isl_take isl_multi_aff *maff2)
2099 {
2100 maff1 = isl_multi_aff_add(maff1, maff2);
2101 maff1 = isl_multi_aff_gist(maff1, isl_set_copy(dom));
2102 return maff1;
2103 }
2104
2105 int isl_multi_aff_is_empty(__isl_keep isl_multi_aff *maff)
2106 {
2107 if (!maff)
2108 return -1;
2109
2110 return 0;
2111 }
2112
2113 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
2114 __isl_keep isl_multi_aff *maff2)
2115 {
2116 int i;
2117 int equal;
2118
2119 if (!maff1 || !maff2)
2120 return -1;
2121 if (maff1->n != maff2->n)
2122 return 0;
2123 equal = isl_space_is_equal(maff1->space, maff2->space);
2124 if (equal < 0 || !equal)
2125 return equal;
2126
2127 for (i = 0; i < maff1->n; ++i) {
2128 equal = isl_aff_plain_is_equal(maff1->p[i], maff2->p[i]);
2129 if (equal < 0 || !equal)
2130 return equal;
2131 }
2132
2133 return 1;
2134 }
2135
2136 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
2137 __isl_take isl_multi_aff *maff,
2138 enum isl_dim_type type, unsigned pos, const char *s)
2139 {
2140 int i;
2141
2142 maff = isl_multi_aff_cow(maff);
2143 if (!maff)
2144 return NULL;
2145
2146 maff->space = isl_space_set_dim_name(maff->space, type, pos, s);
2147 if (!maff->space)
2148 return isl_multi_aff_free(maff);
2149 for (i = 0; i < maff->n; ++i) {
2150 maff->p[i] = isl_aff_set_dim_name(maff->p[i], type, pos, s);
2151 if (!maff->p[i])
2152 return isl_multi_aff_free(maff);
2153 }
2154
2155 return maff;
2156 }
2157
2158 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(__isl_take isl_multi_aff *maff,
2159 enum isl_dim_type type, unsigned first, unsigned n)
2160 {
2161 int i;
2162
2163 maff = isl_multi_aff_cow(maff);
2164 if (!maff)
2165 return NULL;
2166
2167 maff->space = isl_space_drop_dims(maff->space, type, first, n);
2168 if (!maff->space)
2169 return isl_multi_aff_free(maff);
2170
2171 if (type == isl_dim_out) {
2172 for (i = 0; i < n; ++i)
2173 isl_aff_free(maff->p[first + i]);
2174 for (i = first; i + n < maff->n; ++i)
2175 maff->p[i] = maff->p[i + n];
2176 maff->n -= n;
2177 return maff;
2178 }
2179
2180 for (i = 0; i < maff->n; ++i) {
2181 maff->p[i] = isl_aff_drop_dims(maff->p[i], type, first, n);
2182 if (!maff->p[i])
2183 return isl_multi_aff_free(maff);
2184 }
2185
2186 return maff;
2187 }
2188
2189 #undef PW
2190 #define PW isl_pw_multi_aff
2191 #undef EL
2192 #define EL isl_multi_aff
2193 #undef EL_IS_ZERO
2194 #define EL_IS_ZERO is_empty
2195 #undef ZERO
2196 #define ZERO empty
2197 #undef IS_ZERO
2198 #define IS_ZERO is_empty
2199 #undef FIELD
2200 #define FIELD maff
2201 #undef DEFAULT_IS_ZERO
2202 #define DEFAULT_IS_ZERO 0
2203
2204 #define NO_NEG
2205 #define NO_EVAL
2206 #define NO_OPT
2207 #define NO_INVOLVES_DIMS
2208 #define NO_MOVE_DIMS
2209 #define NO_INSERT_DIMS
2210 #define NO_LIFT
2211 #define NO_MORPH
2212
2213 #include <isl_pw_templ.c>
2214
2215 static __isl_give isl_pw_multi_aff *pw_multi_aff_add(
2216 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
2217 {
2218 return isl_pw_multi_aff_on_shared_domain(pma1, pma2,
2219 &isl_multi_aff_add);
2220 }
2221
2222 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
2223 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
2224 {
2225 return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
2226 &pw_multi_aff_add);
2227 }
2228
2229 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
2230 __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
2231 {
2232 return isl_pw_multi_aff_union_add_(pma1, pma2);
2233 }
2234
2235 /* Construct a map mapping the domain the piecewise multi-affine expression
2236 * to its range, with each dimension in the range equated to the
2237 * corresponding affine expression on its cell.
2238 */
2239 __isl_give isl_map *isl_map_from_pw_multi_aff(__isl_take isl_pw_multi_aff *pma)
2240 {
2241 int i;
2242 isl_map *map;
2243
2244 if (!pma)
2245 return NULL;
2246
2247 map = isl_map_empty(isl_pw_multi_aff_get_space(pma));
2248
2249 for (i = 0; i < pma->n; ++i) {
2250 isl_multi_aff *maff;
2251 isl_basic_map *bmap;
2252 isl_map *map_i;
2253
2254 maff = isl_multi_aff_copy(pma->p[i].maff);
2255 bmap = isl_basic_map_from_multi_aff(maff);
2256 map_i = isl_map_from_basic_map(bmap);
2257 map_i = isl_map_intersect_domain(map_i,
2258 isl_set_copy(pma->p[i].set));
2259 map = isl_map_union_disjoint(map, map_i);
2260 }
2261
2262 isl_pw_multi_aff_free(pma);
2263 return map;
2264 }
2265
2266 __isl_give isl_set *isl_set_from_pw_multi_aff(__isl_take isl_pw_multi_aff *pma)
2267 {
2268 if (!isl_space_is_set(pma->dim))
2269 isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
2270 "isl_pw_multi_aff cannot be converted into an isl_set",
2271 return isl_pw_multi_aff_free(pma));
2272
2273 return isl_map_from_pw_multi_aff(pma);
2274 }
2275
2276 /* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map.
2277 * This obivously only works if the input "map" is single-valued.
2278 * If so, we compute the lexicographic minimum of the image in the form
2279 * of an isl_pw_multi_aff. Since the image is unique, it is equal
2280 * to its lexicographic minimum.
2281 * If the input is not single-valued, we produce an error.
2282 */
2283 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(__isl_take isl_map *map)
2284 {
2285 int i;
2286 int sv;
2287 isl_pw_multi_aff *pma;
2288
2289 if (!map)
2290 return NULL;
2291
2292 sv = isl_map_is_single_valued(map);
2293 if (sv < 0)
2294 goto error;
2295 if (!sv)
2296 isl_die(isl_map_get_ctx(map), isl_error_invalid,
2297 "map is not single-valued", goto error);
2298 map = isl_map_make_disjoint(map);
2299 if (!map)
2300 return NULL;
2301
2302 pma = isl_pw_multi_aff_empty(isl_map_get_space(map));
2303
2304 for (i = 0; i < map->n; ++i) {
2305 isl_pw_multi_aff *pma_i;
2306 isl_basic_map *bmap;
2307 bmap = isl_basic_map_copy(map->p[i]);
2308 pma_i = isl_basic_map_lexmin_pw_multi_aff(bmap);
2309 pma = isl_pw_multi_aff_add_disjoint(pma, pma_i);
2310 }
2311
2312 isl_map_free(map);
2313 return pma;
2314 error:
2315 isl_map_free(map);
2316 return NULL;
2317 }
2318
2319 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(__isl_take isl_set *set)
2320 {
2321 return isl_pw_multi_aff_from_map(set);
2322 }
2323
2324 /* Plug in "subs" for dimension "type", "pos" of "aff".
2325 *
2326 * Let i be the dimension to replace and let "subs" be of the form
2327 *
2328 * f/d
2329 *
2330 * and "aff" of the form
2331 *
2332 * (a i + g)/m
2333 *
2334 * The result is
2335 *
2336 * floor((a f + d g')/(m d))
2337 *
2338 * where g' is the result of plugging in "subs" in each of the integer
2339 * divisions in g.
2340 */
2341 __isl_give isl_aff *isl_aff_substitute(__isl_take isl_aff *aff,
2342 enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs)
2343 {
2344 isl_ctx *ctx;
2345 isl_int v;
2346
2347 aff = isl_aff_cow(aff);
2348 if (!aff || !subs)
2349 return isl_aff_free(aff);
2350
2351 ctx = isl_aff_get_ctx(aff);
2352 if (!isl_space_is_equal(aff->ls->dim, subs->ls->dim))
2353 isl_die(ctx, isl_error_invalid,
2354 "spaces don't match", return isl_aff_free(aff));
2355 if (isl_local_space_dim(subs->ls, isl_dim_div) != 0)
2356 isl_die(ctx, isl_error_unsupported,
2357 "cannot handle divs yet", return isl_aff_free(aff));
2358
2359 aff->ls = isl_local_space_substitute(aff->ls, type, pos, subs);
2360 if (!aff->ls)
2361 return isl_aff_free(aff);
2362
2363 aff->v = isl_vec_cow(aff->v);
2364 if (!aff->v)
2365 return isl_aff_free(aff);
2366
2367 pos += isl_local_space_offset(aff->ls, type);
2368
2369 isl_int_init(v);
2370 isl_int_set(v, aff->v->el[1 + pos]);
2371 isl_int_set_si(aff->v->el[1 + pos], 0);
2372 isl_seq_combine(aff->v->el + 1, subs->v->el[0], aff->v->el + 1,
2373 v, subs->v->el + 1, subs->v->size - 1);
2374 isl_int_mul(aff->v->el[0], aff->v->el[0], subs->v->el[0]);
2375 isl_int_clear(v);
2376
2377 return aff;
2378 }
2379
2380 /* Plug in "subs" for dimension "type", "pos" in each of the affine
2381 * expressions in "maff".
2382 */
2383 __isl_give isl_multi_aff *isl_multi_aff_substitute(
2384 __isl_take isl_multi_aff *maff, enum isl_dim_type type, unsigned pos,
2385 __isl_keep isl_aff *subs)
2386 {
2387 int i;
2388
2389 maff = isl_multi_aff_cow(maff);
2390 if (!maff || !subs)
2391 return isl_multi_aff_free(maff);
2392
2393 if (type == isl_dim_in)
2394 type = isl_dim_set;
2395
2396 for (i = 0; i < maff->n; ++i) {
2397 maff->p[i] = isl_aff_substitute(maff->p[i], type, pos, subs);
2398 if (!maff->p[i])
2399 return isl_multi_aff_free(maff);
2400 }
2401
2402 return maff;
2403 }
2404
2405 /* Plug in "subs" for dimension "type", "pos" of "pma".
2406 *
2407 * pma is of the form
2408 *
2409 * A_i(v) -> M_i(v)
2410 *
2411 * while subs is of the form
2412 *
2413 * v' = B_j(v) -> S_j
2414 *
2415 * Each pair i,j such that C_ij = A_i \cap B_i is non-empty
2416 * has a contribution in the result, in particular
2417 *
2418 * C_ij(S_j) -> M_i(S_j)
2419 *
2420 * Note that plugging in S_j in C_ij may also result in an empty set
2421 * and this contribution should simply be discarded.
2422 */
2423 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_substitute(
2424 __isl_take isl_pw_multi_aff *pma, enum isl_dim_type type, unsigned pos,
2425 __isl_keep isl_pw_aff *subs)
2426 {
2427 int i, j, n;
2428 isl_pw_multi_aff *res;
2429
2430 if (!pma || !subs)
2431 return isl_pw_multi_aff_free(pma);
2432
2433 n = pma->n * subs->n;
2434 res = isl_pw_multi_aff_alloc_size(isl_space_copy(pma->dim), n);
2435
2436 for (i = 0; i < pma->n; ++i) {
2437 for (j = 0; j < subs->n; ++j) {
2438 isl_set *common;
2439 isl_multi_aff *res_ij;
2440 common = isl_set_intersect(
2441 isl_set_copy(pma->p[i].set),
2442 isl_set_copy(subs->p[j].set));
2443 common = isl_set_substitute(common,
2444 type, pos, subs->p[j].aff);
2445 if (isl_set_plain_is_empty(common)) {
2446 isl_set_free(common);
2447 continue;
2448 }
2449
2450 res_ij = isl_multi_aff_substitute(
2451 isl_multi_aff_copy(pma->p[i].maff),
2452 type, pos, subs->p[j].aff);
2453
2454 res = isl_pw_multi_aff_add_piece(res, common, res_ij);
2455 }
2456 }
2457
2458 isl_pw_multi_aff_free(pma);
2459 return res;
2460 }
2461
2462 /* Extend the local space of "dst" to include the divs
2463 * in the local space of "src".
2464 */
2465 __isl_give isl_aff *isl_aff_align_divs(__isl_take isl_aff *dst,
2466 __isl_keep isl_aff *src)
2467 {
2468 isl_ctx *ctx;
2469 int *exp1 = NULL;
2470 int *exp2 = NULL;
2471 isl_mat *div;
2472
2473 if (!src || !dst)
2474 return isl_aff_free(dst);
2475
2476 ctx = isl_aff_get_ctx(src);
2477 if (!isl_space_is_equal(src->ls->dim, dst->ls->dim))
2478 isl_die(ctx, isl_error_invalid,
2479 "spaces don't match", goto error);
2480
2481 if (src->ls->div->n_row == 0)
2482 return dst;
2483
2484 exp1 = isl_alloc_array(ctx, int, src->ls->div->n_row);
2485 exp2 = isl_alloc_array(ctx, int, dst->ls->div->n_row);
2486 if (!exp1 || !exp2)
2487 goto error;
2488
2489 div = isl_merge_divs(src->ls->div, dst->ls->div, exp1, exp2);
2490 dst = isl_aff_expand_divs(dst, div, exp2);
2491 free(exp1);
2492 free(exp2);
2493
2494 return dst;
2495 error:
2496 free(exp1);
2497 free(exp2);
2498 return isl_aff_free(dst);
2499 }
2500
2501 /* Adjust the local spaces of the affine expressions in "maff"
2502 * such that they all have the save divs.
2503 */
2504 __isl_give isl_multi_aff *isl_multi_aff_align_divs(
2505 __isl_take isl_multi_aff *maff)
2506 {
2507 int i;
2508
2509 if (!maff)
2510 return NULL;
2511 if (maff->n == 0)
2512 return maff;
2513 maff = isl_multi_aff_cow(maff);
2514 if (!maff)
2515 return NULL;
2516
2517 for (i = 1; i < maff->n; ++i)
2518 maff->p[0] = isl_aff_align_divs(maff->p[0], maff->p[i]);
2519 for (i = 1; i < maff->n; ++i) {
2520 maff->p[i] = isl_aff_align_divs(maff->p[i], maff->p[0]);
2521 if (!maff->p[i])
2522 return isl_multi_aff_free(maff);
2523 }
2524
2525 return maff;
2526 }
2527
2528 __isl_give isl_aff *isl_aff_lift(__isl_take isl_aff *aff)
2529 {
2530 aff = isl_aff_cow(aff);
2531 if (!aff)
2532 return NULL;
2533
2534 aff->ls = isl_local_space_lift(aff->ls);
2535 if (!aff->ls)
2536 return isl_aff_free(aff);
2537
2538 return aff;
2539 }
2540
2541 /* Lift "maff" to a space with extra dimensions such that the result
2542 * has no more existentially quantified variables.
2543 * If "ls" is not NULL, then *ls is assigned the local space that lies
2544 * at the basis of the lifting applied to "maff".
2545 */
2546 __isl_give isl_multi_aff *isl_multi_aff_lift(__isl_take isl_multi_aff *maff,
2547 __isl_give isl_local_space **ls)
2548 {
2549 int i;
2550 isl_space *space;
2551 unsigned n_div;
2552
2553 if (ls)
2554 *ls = NULL;
2555
2556 if (!maff)
2557 return NULL;
2558
2559 if (maff->n == 0) {
2560 if (ls) {
2561 isl_space *space = isl_multi_aff_get_domain_space(maff);
2562 *ls = isl_local_space_from_space(space);
2563 if (!*ls)
2564 return isl_multi_aff_free(maff);
2565 }
2566 return maff;
2567 }
2568
2569 maff = isl_multi_aff_cow(maff);
2570 maff = isl_multi_aff_align_divs(maff);
2571 if (!maff)
2572 return NULL;
2573
2574 n_div = isl_aff_dim(maff->p[0], isl_dim_div);
2575 space = isl_multi_aff_get_space(maff);
2576 space = isl_space_lift(isl_space_domain(space), n_div);
2577 space = isl_space_extend_domain_with_range(space,
2578 isl_multi_aff_get_space(maff));
2579 if (!space)
2580 return isl_multi_aff_free(maff);
2581 isl_space_free(maff->space);
2582 maff->space = space;
2583
2584 if (ls) {
2585 *ls = isl_aff_get_domain_local_space(maff->p[0]);
2586 if (!*ls)
2587 return isl_multi_aff_free(maff);
2588 }
2589
2590 for (i = 0; i < maff->n; ++i) {
2591 maff->p[i] = isl_aff_lift(maff->p[i]);
2592 if (!maff->p[i])
2593 goto error;
2594 }
2595
2596 return maff;
2597 error:
2598 if (ls)
2599 isl_local_space_free(*ls);
2600 return isl_multi_aff_free(maff);
2601 }
2602
2603
2604 /* Extract an isl_pw_aff corresponding to output dimension "pos" of "pma".
2605 */
2606 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
2607 __isl_keep isl_pw_multi_aff *pma, int pos)
2608 {
2609 int i;
2610 int n_out;
2611 isl_space *space;
2612 isl_pw_aff *pa;
2613
2614 if (!pma)
2615 return NULL;
2616
2617 n_out = isl_pw_multi_aff_dim(pma, isl_dim_out);
2618 if (pos < 0 || pos >= n_out)
2619 isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
2620 "index out of bounds", return NULL);
2621
2622 space = isl_pw_multi_aff_get_space(pma);
2623 space = isl_space_drop_dims(space, isl_dim_out,
2624 pos + 1, n_out - pos - 1);
2625 space = isl_space_drop_dims(space, isl_dim_out, 0, pos);
2626
2627 pa = isl_pw_aff_alloc_size(space, pma->n);
2628 for (i = 0; i < pma->n; ++i) {
2629 isl_aff *aff;
2630 aff = isl_multi_aff_get_aff(pma->p[i].maff, pos);
2631 pa = isl_pw_aff_add_piece(pa, isl_set_copy(pma->p[i].set), aff);
2632 }
2633
2634 return pa;
2635 }
Integer set library